I I 22 APPENDICES AND TABLES 



B/ = 



(xiv) 



1 14 I ' 



2' 8 3 



r\ 



Similarly 



By (xii) and (xiii) ., 



o o 



2 X 



This is larger by ^- g inch than the result obtained by (xiv). 

 The following is an example worthy of note. Suppose 



t 



Thus let r = 5 -. s = 5, t = 1, /* =|. 



2 2 



5C-- "l - 



Then by (xiv) B/==_i 2 _-= = -310. 



2 \2~sJ 12 



It will be observed that, although this meniscus is thickest in the 

 middle, it has, however, a large negative focus. 



The principal points of a sphere are at its centre. 

 The focus of a sphere, measured from the centre : 



The focus of a sphere measured from its surface : 



Bf= l~I (SYi) 



The focus of a hemisphere measured from the plane surface, the light 

 being incident on the convex surface : 



B/= (vi) 



But when the light is incident on the plane surface, the lens being 

 turned round : 



B/= 11 . . . ... (iv) 



When p. = 1'5 the focus of a sphere measured from the surface = A the 

 radius. 



The focus of a hemisphere measured from the plane side = 1^ the 

 radius, and when measured from the convex side the focus =- 2 radii. 



In a cylindrical lens the principal points cross over. 



To find the radii r and s of a crossed lens of minimum aberration for 

 parallel rays : 



